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SCIENCE. 



[N. S. Vol. XXII. No. 556. 



ment in this range of thought is the mathe- 

 matical development of the Newtonian 

 theory of gravitation applied to the whole 

 universe. It -was made, in the main, by 

 Lagrange, as regards the wider theory, and 

 by Laplace, as regards the amplitude of 

 detailed application. But it was a century 

 that also saw the obliteration of the ancient 

 doctrines of caloric and phlogiston, 

 through the discoveries of Rumford and 

 Davy of the nature and relations of heat. 

 The modern science of vibrations had its 

 beginnings in the experiments of Chladni, 

 and, as has already been stated, the un- 

 dulatory theory of light was rehabilitated 

 by the researches of Thomas Young. 

 Strange views as to the physical constitu- 

 tion of the universe then were sent to the 

 limbo of forgotten ignorance by the early 

 discoveries of modern chemistry ; and engi- 

 neering assumed a systematic and scientific 

 activity, the limits of which seem bounded 

 only by the cumulative ingenuity of succes- 

 sive generations. But in thus attempting 

 to summarize the progress of science in 

 that period, I appear to be trespassing upon 

 the domains of other sections; my steps 

 had better be retraced so as to let us return 

 to our own upper air. If I mention one 

 more fact (and it will be a small one), it is 

 because of its special connection with the 

 work of this section. As you are aware, the 

 elements of Euclid have long been the 

 standard treatise of elementary geometry 

 in Great Britain; and the Greek methods, 

 in Robert Simson's edition, have been im- 

 posed upon candidates in examination after 

 examination. But Euclid is on the verge of 

 being disestablished ; my own University of 

 Cambridge, which has had its full share in 

 maintaining the restriction to Euclid's 

 methods, and which was not uninfluenced 

 by the report of a committee of this associa- 

 tion upon the subject, will, some six or seven 

 weeks hence, hold its last examination in 



which those methods are prescriptively re- 

 quired. The disestablishment of Euclid 

 from tyranny over the youthful student 

 on the continent of Europe was effected be- 

 fore the end of the eighteenth century. 



But it is time for me to pass on to the 

 third of the centenaries, with which the 

 present year can be associated. Not so fun- 

 damental for the initiation of modern sci- 

 ence as was the year in which the ' Advance- 

 ment of Learning ' was published, not so 

 romantic in the progress of modern science 

 as was the year in which Halley gave his 

 prediction to the world, the year 1805 (tur- 

 bulent as it was with the strife of European 

 politics) is marked by the silent voices of a 

 couple of scientific records. . In that year 

 Laplace published the last progressive in- 

 stalment of his great treatise on ' Celestial 

 Mechanics,' the portion that still remained 

 for the future being solely of an historical 

 character; the great number of astronom- 

 ical phenomena which he had been able to 

 explain by his mathematical presentation 

 of the consequences of the Newtonian 

 theory would, by themselves, have been suf- 

 ficient to give confidence in the validity of 

 that theory. In that year also Monge pub- 

 lished his treatise, classical and still to be 

 read by all students of the subject, ' The 

 Application of Algebra to Geometry ' ; it 

 is the starting point of modern synthetic 

 geometry, which has marched in ample de- 

 velopment since his day. These are but 

 landmarks in the history of mathematical 

 science, one of them indicating the com- 

 pleted attainment of a tremendous task, the 

 other of them initiating a new departure ; 

 both of them have their significance in the 

 progress of their respective sciences. 



When we contemplate the activity and 

 the achievements of the century that has 

 elapsed since the stages which have just 

 been mentioned were attained in mathe- 

 matical science, the amount, the variety, the 



